Highest Common Factor of 690, 454, 101 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 690, 454, 101 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 690, 454, 101 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 690, 454, 101 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 690, 454, 101 is 1.

HCF(690, 454, 101) = 1

HCF of 690, 454, 101 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 690, 454, 101 is 1.

Highest Common Factor of 690,454,101 using Euclid's algorithm

Highest Common Factor of 690,454,101 is 1

Step 1: Since 690 > 454, we apply the division lemma to 690 and 454, to get

690 = 454 x 1 + 236

Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 236 and 454, to get

454 = 236 x 1 + 218

Step 3: We consider the new divisor 236 and the new remainder 218, and apply the division lemma to get

236 = 218 x 1 + 18

We consider the new divisor 218 and the new remainder 18,and apply the division lemma to get

218 = 18 x 12 + 2

We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get

18 = 2 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 690 and 454 is 2

Notice that 2 = HCF(18,2) = HCF(218,18) = HCF(236,218) = HCF(454,236) = HCF(690,454) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 101 > 2, we apply the division lemma to 101 and 2, to get

101 = 2 x 50 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 101 is 1

Notice that 1 = HCF(2,1) = HCF(101,2) .

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Frequently Asked Questions on HCF of 690, 454, 101 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 690, 454, 101?

Answer: HCF of 690, 454, 101 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 690, 454, 101 using Euclid's Algorithm?

Answer: For arbitrary numbers 690, 454, 101 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.